簡約 [3(2x-3y)]^2+[4(2x+3y)]^2

解

簡約

[3 (2 x - 3 y)]^{2} + [4 (2 x + 3 y)]^{2}

100 x^{2} + 84 x y + 225 y^{2}

解答ステップ

(3 (2 x - 3 y))^{2} + (4 (2 x + 3 y))^{2}

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

= 3^{2} (2 x - 3 y)^{2} + (4 (2 x + 3 y))^{2}

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

= 3^{2} (2 x - 3 y)^{2} + 4^{2} (2 x + 3 y)^{2}

改良

= 9 (2 x - 3 y)^{2} + 16 (2 x + 3 y)^{2}

(2 x - 3 y)^{2} : 4 x^{2} - 12 x y + 9 y^{2}

= 9 (4 x^{2} - 12 x y + 9 y^{2}) + 16 (2 x + 3 y)^{2}

(2 x + 3 y)^{2} : 4 x^{2} + 12 x y + 9 y^{2}

= 9 (4 x^{2} - 12 x y + 9 y^{2}) + 16 (4 x^{2} + 12 x y + 9 y^{2})

拡張

9 (4 x^{2} - 12 x y + 9 y^{2}) : 36 x^{2} - 108 x y + 81 y^{2}

= 36 x^{2} - 108 x y + 81 y^{2} + 16 (4 x^{2} + 12 x y + 9 y^{2})

拡張

16 (4 x^{2} + 12 x y + 9 y^{2}) : 64 x^{2} + 192 x y + 144 y^{2}

= 36 x^{2} - 108 x y + 81 y^{2} + 64 x^{2} + 192 x y + 144 y^{2}

簡素化

36 x^{2} - 108 x y + 81 y^{2} + 64 x^{2} + 192 x y + 144 y^{2} : 100 x^{2} + 84 x y + 225 y^{2}

= 100 x^{2} + 84 x y + 225 y^{2}